What effect does the concentration of H+ ions have on the nature of the solution?

The concentration of H⁺ ions increases the acidity of any solution i.e. more the [H⁺],more the acidity.

Yes, basic solutions also have H⁺ ions, it is only that in basic solutions, [OH^-]> [H⁺] i.e. more hydroxyl hence tends to be basic.

Quick lime,CaO is basic in nature so a farmer will treat soil with it only if it is acidic.

Hence, the answers to each part can be summarised as follows:

 [H⁺]-Makes sol. acidic

Basic solutions have  [H⁺] but are basic because [OH^-]> [H⁺].

CaO treatment under acidic condition